What are the most important components in the algorithm of a minimum AI?
Some good places to start would be cognitive architectures and as mentioned in another answer intelligent agents. The question is broad but you definitely want to look into planning &amp; decision making. You might also want to check out the L5 and L6 layers of Hierarchical Temporal Memory (As in Nupic) as it relates to feedback, behavior and attention.

If I were you I'd aim for more cognitive solutions (I realize that term is a bit ambiguous itself when we talk about machines). There's also new AI initiative going on involving probabilistic programming. See Probabilistic Models of Cognition made by Goodman (Stanford University) and Tenenbaum (MIT) or Anglican made by Wood (University of Oxford) et al.